Thresholds, Weber’s law, Fechner’s three methods Research Methods Fall 2010 Tamás Bőhm

Introspection Method applied by early psychologists (Wundt) Self-observation of conscious thoughts and sensations –Do I perceive this light brighter than that? Why? Inherently subjective  rejected as a scientific method But it provides useful intuitions when designing experiments (helps forming hypotheses) –I realized that it is hard for me to hear very high and very low tones. Thus the frequency of a tone may be a factor in its perceived loudness/audibility. Let’s test this in an experiment!

Formal methods Quantifying the sensations evoked by physical stimuli Gustav Fechner (1860): established 3 formal psychophysical methods Fechner’s methods have been (and are being) widely used More reliable and accurate than introspection Results from different experiments are comparable

Thresholds If a linear relationship is assumed, two values determine the function: –X-intercept: minimum stimulus value that evoked any sensation; absolute threshold –Slope: the rate at which sensation grows as we increase intensity; difference threshold (inversely proportional to slope) Stimulus intensity Sensation magnitude Linear psychophysical equation X-intercept slope

Thresholds General definitions (not assuming linearity): –Absolute threshold: intensity that the observer can just barely detect Intensities below absolute threshold: undetectable Intensities above absolute threshold: detectable –Difference threshold (aka. just noticeable difference /JND/ and difference limen): minimum intensity difference that is noticeable to the observer A change in intensity that is smaller than the difference threshold: undetectable A change in intensity that is larger than the difference threshold: detectable

Difference thresholds Linear function  difference threshold (slope) is constant An observer able to detect the difference between intensities 100 and 110 should also be able to detect the difference between 1000 and This is not the case: the observer is able to detect the difference only between 1000 and & 550 Hz tones 5000 & 5050 Hz tones 5000 & 5500 Hz tones Difference threshold is not constant! Stimulus intensity Sensation magnitude Linear psychophysical equation constant slope

Difference thresholds Difference threshold is not constant (changes with intensity)  function is nonlinear Weber’s law: difference threshold is a constant proportion of the initial stimulus value ΔI / I = c Previous examples: c=10% Weber’s law holds only approximately! Stimulus intensity Sensation magnitude Nonlinear psychophysical equation slope changes with intensity

Absolute thresholds Even in the absence of stimulation, there is some random firing on sensory nerves This inner noise can even vary from moment to moment Observers cannot distinguish inner noise from the effect of a weak stimulus Even when there is no light (perfect darkness), observers may experience a dim light (dark light, intrinsic light) Observers in an anechoic chamber often report hearing a whistling sound  Measuring truly „absolute” thresholds is problematic: observers may confuse inner noise with the real thing

Psychophysical methods Threshold measurements: detection of small intensities (absolute thr.) and discrimination of small intensity differences (difference thr.) Is it intense enough to see? How small a difference can you see? –Fechner’s 3 methods Method of constant stimuli Method of limits Method of adjustment –Modifications of Fechner’s methods Staircase method Modifications of the method of constant stimuli (adaptive, no standard) –Forced choice, objective methods –Sensory decision theory (SDT) –Psychophysical functions from psychometric data Direct scaling: growth of sensation with intensity How bright do you see a light? –Magnitude estimation and the power law Multidimensional scaling: degree to which stimuli are comparable along some dimensions Along which dimensions do you judge the similarity of two stimuli?

Fechner’s three methods Presenting one stimulus at a time The stimulus is very weak Possible responses: “Yes, I see it.” / “No, I don’t see it.” Absolute thresholdDifference threshold Method of constant stimuli  Method of limits  Method of adjustment  not used Presenting two stimuli at a time: –Standard: fixed, easily detectable –Comparison: either more or less intense than the standard Possible responses: “Comparison is stronger.” / “Comparison is weaker.”

Method of constant stimuli for measuring absolute thresholds 1.Select a range of light intensities from certainly invisible to certainly visible 2.Pick a few (4-7) points uniformly in this intensity range; this will be the constant stimulus set WeakStrong Light intensity

Method of constant stimuli for measuring absolute thresholds 3.Test each stimulus many times (20-25) in random order …

Method of constant stimuli for measuring absolute thresholds 4.Present the stimuli one at a time and ask the observer if it was visible or not Visible? YESNO

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Could you see the spot of light?

Method of constant stimuli for measuring absolute thresholds 5.Calculate the proportion of “yes” and “no” responses at each light level %5%20%50%80%95%100%

Method of constant stimuli for measuring absolute thresholds 6.Plot the percentages against stimulus intensity  psychometric function Stimulus intensity Percentage “seen” 0% 100% 50% 75% 25%

Psychometric function for absolute thresholds Ideal FIG (Sekuler) Fixed absolute threshold Step function Actual FIG (Sekuler) Absolute threshold varies somewhat from trial to trial (due to constant fluctuations in sensitivity) Conventionally, the intensity corresponding to 50% is considered to be the threshold sigmoid function

Method of constant stimuli for measuring difference thresholds 1.Standard stimulus has a fixed intensity 2.The intensities of comparison stimuli bracket the standard Light intensity Standard stimulus: Comparison stimuli:

Method of constant stimuli for measuring difference thresholds 3.All pairs of standard and comparison stimuli are tested many times

Method of constant stimuli for measuring difference thresholds 4.For each pair, the observer judges if the comparison stimulus was stronger or weaker than the standard STRONGERWEAKER

Method of constant stimuli for measuring difference thresholds 5.For each comparison level, the percentage of “stronger” responses is calculated and results are plotted as a psychometric function Light intensity of comparison stimuli Percentage “stronger” 0% 100% 50% 75% 25%

Psychometric function for difference thresholds When the observer cannot see a difference, he/she chooses randomly between “stronger” and “weaker”; this corresponds to 50% on the psychometric function  point of subjective equivalence (PSE) Light intensity of comparison stimuli Percentage “stronger” 0% 100% 50% 75% 25% PSE

Psychometric function for difference thresholds By convention, the intensity at 75% is considered to be just noticeably stronger than the standard  DS A comparison intensity at 25% is just noticeably weaker than the standard  DW Difference threshold = the average of DS and DW Light intensity of comparison stimuli Percentage “stronger” 0% 100% 50% 75% 25% DW DS

Psychometric function for difference thresholds

Method of limits for measuring absolute thresholds 1.On each trial, the observer reports if she/he could see the light or not. 2.Start with presenting a light intensity well above the expected threshold (the observer can certainly see it) 3.Decrease the intensity until the observer cannot see it 4.Threshold estimate: the intensity at which the response changes Light intensity Trials Descending series: start from above the expected threshold and decrease intensity Ascending series: start from below the expected threshold and increase intensity threshold estimate

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Method of limits for measuring absolute thresholds Ascending and descending series may yield different results  use both Even in the same direction, there is variability in the threshold (inner noise, etc)  average many measurements Measured threshold corresponds to 50% point in a psychometric function (method of constant stimuli) Light intensity Trials pure-tone audiometry

threshold estimate Method of limits for measuring difference thresholds Intensity of the comparison stimulus is decreased (descending) or increased (ascending) until the response changes Threshold estimate: intensity difference between the standard and comparison stimuli where the response changes Average results from multiple series in both directions Light intensity of comparison stimulus Trials +comparison brighter -comparison weaker

Method of adjustment for measuring absolute thresholds Observer can vary the stimulus intensity Instructed to adjust it so that it is just visible or just invisible Initial intensity is set to be far from the expected threshold value adjustment device stimulus with adjusted intensity observer

Method of adjustment for measuring absolute thresholds Threshold estimate: final intensity value Descending: initial intensity is well above expected threshold; adjusted to just visible Ascending: initially well below threshold; adjusted to just invisible Ascending and descending task repeated several times and results averaged Similar to method of limits but observers find it easier threshold estimate descending ascending Adjustment: by a real or a software device (e.g. knob, slider)